Entropy in dynamical systems
"This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon-McMillan-Breiman Theorem, the Ornstein-Weiss Return Time Theorem, the Krieger...
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| Main Author: | |
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| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York :
Cambridge University Press,
2011.
|
| Series: | New mathematical monographs ;
18. |
| Subjects: | |
| Online Access: | An electronic book accessible through the World Wide Web; click to view |
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| 007 | cr cn||||||||| | ||
| 008 | 101129s2011 enk sb 001 0 eng d | ||
| 010 | |z 2010050336 | ||
| 020 | |z 9780521888851 (hardback) | ||
| 020 | |z 9781139185677 (e-book) | ||
| 040 | |a CaPaEBR |c CaPaEBR | ||
| 035 | |a (OCoLC)774385269 | ||
| 050 | 1 | 4 | |a QA611.5 |b .D685 2011eb |
| 082 | 0 | 4 | |a 515/.39 |2 22 |
| 100 | 1 | |a Downarowicz, Tomasz, |d 1956- | |
| 245 | 1 | 0 | |a Entropy in dynamical systems |h [electronic resource] / |c Tomasz Downarowicz. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2011. | ||
| 300 | |a xii, 391 p. | ||
| 490 | 1 | |a New mathematical monographs ; |v 18 | |
| 504 | |a Includes bibliographical references (p. [379]-385) and index. | ||
| 505 | 8 | |a Machine generated contents note: Introduction; Part I. Entropy in Ergodic Theory: 1. Shannon information and entropy; 2. Dynamical entropy of a process; 3. Entropy theorems in processes; 4. Kolmogorov-Sinai entropy; 5. The ergodic law of series; Part II. Entropy in Topological Dynamics: 6. Topological entropy; 7. Dynamics in dimension zero; 8. The entropy structure; 9. Symbolic extensions; 10. A touch of smooth dynamics; Part III. Entropy Theory for Operators: 11. Measure theoretic entropy of stochastic operators; 12. Topological entropy of a Markov operator; 13. Open problems in operator entropy; Appendix A. Toolbox; Appendix B. Conditional S-M-B; List of symbols; References; Index. | |
| 520 | |a "This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon-McMillan-Breiman Theorem, the Ornstein-Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research"-- |c Provided by publisher. | ||
| 533 | |a Electronic reproduction. |b Palo Alto, Calif. : |c ebrary, |d 2013. |n Available via World Wide Web. |n Access may be limited to ebrary affiliated libraries. | ||
| 650 | 0 | |a Topological entropy |v Textbooks. | |
| 650 | 0 | |a Topological dynamics |v Textbooks. | |
| 655 | 7 | |a Electronic books. |2 local | |
| 710 | 2 | |a ebrary, Inc. | |
| 830 | 0 | |a New mathematical monographs ; |v 18. | |
| 856 | 4 | 0 | |u http://site.ebrary.com/lib/daystar/Doc?id=10521005 |z An electronic book accessible through the World Wide Web; click to view |
| 999 | |c 196676 |d 196676 | ||